Optimal. Leaf size=18 \[ \frac {x^{3/2}}{3 (b x+2)^{3/2}} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {37} \[ \frac {x^{3/2}}{3 (b x+2)^{3/2}} \]
Antiderivative was successfully verified.
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Rule 37
Rubi steps
\begin {align*} \int \frac {\sqrt {x}}{(2+b x)^{5/2}} \, dx &=\frac {x^{3/2}}{3 (2+b x)^{3/2}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {x^{3/2}}{3 (b x+2)^{3/2}} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 27, normalized size = 1.50 \[ \frac {\sqrt {b x + 2} x^{\frac {3}{2}}}{3 \, {\left (b^{2} x^{2} + 4 \, b x + 4\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.22, size = 82, normalized size = 4.56 \[ \frac {4 \, {\left (3 \, {\left (\sqrt {b x + 2} \sqrt {b} - \sqrt {{\left (b x + 2\right )} b - 2 \, b}\right )}^{4} \sqrt {b} + 4 \, b^{\frac {5}{2}}\right )} {\left | b \right |}}{3 \, {\left ({\left (\sqrt {b x + 2} \sqrt {b} - \sqrt {{\left (b x + 2\right )} b - 2 \, b}\right )}^{2} + 2 \, b\right )}^{3} b^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.72 \[ \frac {x^{\frac {3}{2}}}{3 \left (b x +2\right )^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 12, normalized size = 0.67 \[ \frac {x^{\frac {3}{2}}}{3 \, {\left (b x + 2\right )}^{\frac {3}{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 12, normalized size = 0.67 \[ \frac {x^{3/2}}{3\,{\left (b\,x+2\right )}^{3/2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.40, size = 27, normalized size = 1.50 \[ \frac {x^{\frac {3}{2}}}{3 b x \sqrt {b x + 2} + 6 \sqrt {b x + 2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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